Evolution is
performed on an AMR (Adaptive Mesh Refinement) grid. The outermost grid
is 394 M x 394 M, the innermost refinement level for
the BH is 2.8 M x 2.8 M and the innermost refinement
level for the NS is 3.3 M x 3.3 M. Here M is the
total (ADM) mass of the intial system. The innermost resolution is
ΔXmin/M = 1/32.5 while the outermost is
ΔXmax/M = 3.94. In this simulation, the
initial binary coordinate separation is D0/M = 8.81, the initial angular
momentum of the system is J/M2 =
0.702, the mass ratio is MBH:MNS = 3:1,
and the black hole spin parameter is JBH/MBH2 =
0.00. (Note: The open circle in the lower right-hand corner of
the above figure is a clock.)

Evolution
of the Density Profile

In the clip from the equatorial plane, the rest-mass density of the
neutron star is plotted on a logarithmic scale normalized to the initial
central density. The gravitational field is evolved via the BSSN scheme
using "moving puncture" gauge conditions. The relativistic hydrodynamic
equations are solved using a high-resolution shock-capturing (HRSC)
method.

After two orbits the density contours are for
the most part undisturbed. After 3.5 orbits the first few density
contours have crossed into the apparent horizon. The NS tail deforms
into a quasistationary disk, as the bulk of the matter is all accreted
onto the hole in a few periods.

The gravitational wavetrain from
a compact binary system may be separated into three qualitatively
different phases: the inspiral, merger, and ringdown. During the
inspiral phase, which takes up most of the binary's lifetime, gravity
wave emission gradually reduces the binary separation. The merger phase
of the gravitational wavetrain is characterized by tidal disruption of
the neutron star. Finally, ringdown radiation is emitted as the
distorted black hole settles down to Kerr-like equilibrium (Note: Only
in the case of a vacuum spacetime does the spinning BH obey the Kerr
solution. The BHs formed here are surrounded by gaseous disks with
small, but nonnegligible, rest mass). Both polarization modes
(h+ and hx) are shown. Total energy conservation
is obeyed to within 0.02%. Total angular momentum conservation is obeyed to within
2.2%.

Listed in the table below is the dimensionless spin of the
Kerr-like black hole at the end of our simulation. Also shown are the
radiated energy, angular momentum, and linear recoil velocity resulting
from gravitational wave emission. Additional parameters for the disk
are given in the film clip.